# expansion of hot metal

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I assume that metal molecules vibrate more as they get hotter; but their electrons also must also expand and contract more as they absorb and release more photons. My question is whether both or only one (or neither) of these processes (particle vibration and/or electron level increase) is responsible for the volumetric expansion of metal as it heats up?

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In order to get an electron to "expand", you would need to excite it into a higher energy orbtial (typically, the higher the orbital energy, the further it is from the nucleus).

Heat is infar red photons which posses energy relating to their frequency (E=hv). If you calculate the energy that infa red protons have, then it is not enough to excite electrons into higher energy orbitals. For almost all bonds, you need UV light to cause excitation.

Infar red radiation, however, can be absorbed by molecules which results in their bonds vibrating, stretching, bending, etc and is the basis of IR spectroscopy. In terms of a metal, this would translate into the metal atoms vibrating and moving around faster which then corresponds to increase in volume.

Edited by Horza2002
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In order to get an electron to "expand", you would need to excite it into a higher energy orbtial (typically, the higher the orbital energy, the further it is from the nucleus).

Heat is infar red photons which posses energy relating to their frequency (E=hv). If you calculate the energy that infa red protons have, then it is not enough to excite electrons into higher energy orbitals. For almost all bonds, you need UV light to cause excitation.

So infrared photons are not the product of electron-levels jumping and falling, only UV? So when metal absorbs infrared-level heat, it does so purely as molecular vibration?

Infar red radiation, however, can be absorbed by molecules which results in their bonds vibrating, stretching, bending, etc and is the basis of IR spectroscopy. In terms of a metal, this would translate into the metal atoms vibrating and moving around faster which then corresponds to increase in volume.

Ok, you just said that "for almost all bonds, you need UV light to cause excitation" and now you're saying that IR radiation can be absorbed by molecules in a way that causes their bonds to get excited? So would I be correct to conclude that the overall electron orbit-shapes of the atoms/molecules don't cause the metals to expand but their bond-electrons do expand and move more forcefully and this pushes them a bit further apart?

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Ok, you just said that "for almost all bonds, you need UV light to cause excitation" and now you're saying that IR radiation can be absorbed by molecules in a way that causes their bonds to get excited? So would I be correct to conclude that the overall electron orbit-shapes of the atoms/molecules don't cause the metals to expand but their bond-electrons do expand and move more forcefully and this pushes them a bit further apart?

Metals bonded together in a crystal don't have the same electronic behavior as ionic solids or covalent solids. The metal atoms all share share electrons in the conduction band. This isn't something I'm very familiar with as I'm not a solid state chemist. If memory serves, Klaynos knows about solid state physics. See if you can find him.

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mississippichem gave you a simple model recently about molecular bonds: balls attached by a spring. They have some energy so they vibrate. When they system gets hotter there's more energy, so the amplitude of the vibrations increase. The material expands.

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mississippichem gave you a simple model recently about molecular bonds: balls attached by a spring. They have some energy so they vibrate. When they system gets hotter there's more energy, so the amplitude of the vibrations increase. The material expands.

And would it be accurate to say that the conduction bands of metals are a form of intermolecular bonding that vibrates as well and thereby causes expansion as well as decreasing viscosity?

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The conduction band is a description of the energy structure of the electrons. The electrons in that band will have an increase in thermal energy as you increase temperature, but the basic effect of physical expansion is the increased average separation of the nuclei.

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The conduction band is a description of the energy structure of the electrons. The electrons in that band will have an increase in thermal energy as you increase temperature, but the basic effect of physical expansion is the increased average separation of the nuclei.

I took the conduction band to mean that there were relatively "loose" outer electrons in metals because 1) they are very far from the nucleus and 2) the outer shell is relatively empty, which causes them to more easily absorb, re-emit, and liberate. Is this incorrect?

So when you say the average separation of the nuclei increases, do you mean that the nuclei are bonded separately from their conduction-band electrons and that the conduction-band electrons behave relatively independently of the bond-electrons?

Does the increase in thermal energy of the conduction band electrons result in volume-change of those electrons and/or change in the viscosity between molecules?

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So infrared photons are not the product of electron-levels jumping and falling, only UV? So when metal absorbs infrared-level heat, it does so purely as molecular vibration?

Ok, you just said that "for almost all bonds, you need UV light to cause excitation" and now you're saying that IR radiation can be absorbed by molecules in a way that causes their bonds to get excited? So would I be correct to conclude that the overall electron orbit-shapes of the atoms/molecules don't cause the metals to expand but their bond-electrons do expand and move more forcefully and this pushes them a bit further apart?

Ok sorry, I didn't make that clear. Molecules typically have four "types" of energy:

• Translational - the general movement in 3D space of a molecule
• Rotational - the tumbling motion of a molecule through space
• Vibrational - the bending, stretching etc of bonds
• Electronic - moving the electrons between orbitals

In order to make the orbitals bigger, you would need to excite an electron into a higher orbital - that is electronic "energy" and normally requires photons of at least UV frequency.

IR photons can be absorbed by molecules that result in changes in the vibrational state of the system...this does not change which orbitals are occupied.

Mississippichem has said the bands are like springs, they move more when they're hot.

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I took the conduction band to mean that there were relatively "loose" outer electrons in metals because 1) they are very far from the nucleus and 2) the outer shell is relatively empty, which causes them to more easily absorb, re-emit, and liberate. Is this incorrect?

So when you say the average separation of the nuclei increases, do you mean that the nuclei are bonded separately from their conduction-band electrons and that the conduction-band electrons behave relatively independently of the bond-electrons?

Does the increase in thermal energy of the conduction band electrons result in volume-change of those electrons and/or change in the viscosity between molecules?

The conduction band has a higher energy and it's not filled, so it is possible to promote electrons from lower-energy bands to the conduction band. They are easier to liberate, but that's not an effect in play here.

The effect you are asking about (expansion) has little to do with the behavior of the conduction band electrons.

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The conduction band has a higher energy and it's not filled, so it is possible to promote electrons from lower-energy bands to the conduction band. They are easier to liberate, but that's not an effect in play here.

The effect you are asking about (expansion) has little to do with the behavior of the conduction band electrons.

Well, it all seems very interrelated so I'm trying to sort out what is what and how they affect each other. The conduction band electrons are pretty clearly conductive because they are relatively free. Their liberation may be a different phenomena than the promotion of electrons from lower-energy bands but it seems more like there's a gradient of relative freedom of movement as they move away from the nucleus. It also seems as though energy gets generally absorbed and expressed by electrons as kinetic motion and radiation, so the conduction-bands of metal molecules, while they're heating up, would vibrate more, liberate and become fluid more, and emit higher frequencies (according to blackbody emission logic). I also still can't help wondering if these relatively free electrons don't expand somewhat due to the energy increase among them, but I take it the reason you say that the effect is unrelated to the expansion of the material at the observable level is because the bond-vibrations cause much more motion, i.e. between atoms instead of just between electrons.

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I also still can't help wondering if these relatively free electrons don't expand somewhat due to the energy increase among them, but I take it the reason you say that the effect is unrelated to the expansion of the material at the observable level is because the bond-vibrations cause much more motion, i.e. between atoms instead of just between electrons.

Electrons are point particles, so they don't expand. The distance between atoms is what expands, and since almost all of the mass is in the nucleus, it means the distance between nuclei expands, as I've already said. The increased thermal motion of electrons is negligible in looking at the center of mass of the individual atoms.

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I assume that metal molecules vibrate more as they get hotter; but their electrons also must also expand and contract more as they absorb and release more photons. My question is whether both or only one (or neither) of these processes (particle vibration and/or electron level increase) is responsible for the volumetric expansion of metal as it heats up?

1/2 mv^2 = Under root of T (temperature). Increase in temperature results in increase of v...which is velocity of particle.

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Electrons are point particles, so they don't expand. The distance between atoms is what expands, and since almost all of the mass is in the nucleus, it means the distance between nuclei expands, as I've already said. The increased thermal motion of electrons is negligible in looking at the center of mass of the individual atoms.

I'm surprised there's not more expansion of distance between the electrons in the conduction band, free(d) electrons, etc. as energy transmissions among them intensify. The strange thing about the bond-vibrations causing distantiation between the molecules is that the outer (conduction band) electrons would have to mediate the collision force between the vibrating molecules, right? So wouldn't they have to be moving around quite a lot as the atoms vibrate against each other?

btw, are there any metals that don't have bonds; i.e. they exist only as unbonded single atoms, yet still expand when heated?

Edited by lemur
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btw, are there any metals that don't have bonds; i.e. they exist only as unbonded single atoms, yet still expand when heated?

No. The only atoms that don't generally form bonds are the noble gases, and they aren't metals. They do expand when heated, because they obey the ideal gas law.

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No. The only atoms that don't generally form bonds are the noble gases, and they aren't metals. They do expand when heated, because they obey the ideal gas law.

I should have known that, since it's logical, but thanks for pointing it out. How do noble gases behave as liquids/solids? I should go google noble gas behavior, but before I do I should just say the reason I'm wondering is because it seems like the bonds are a special variation of conduction-band electrons that get concentrated between the atoms - because the bonds seem to conduct energy relatively easily like the conduction-band electrons. It leads me to think that bond expansion/contraction (spring-like motion) is a variation of conduction-band level oscillations, only with those conduction-band electrons accumulated and concentrated between the atoms.

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I should go google noble gas behavior, but before I do I should just say the reason I'm wondering is because it seems like the bonds are a special variation of conduction-band electrons that get concentrated between the atoms - because the bonds seem to conduct energy relatively easily like the conduction-band electrons.

Covalent bonds behave very differently from the conduction band in bulk metals. Electrons in most molecular orbitals cannot communicate. Meaning that an electron in said orbital cannot be conducted through the bond to another orbital. The reason for this is quite mathy, but in quantum chemical treatments we have these things called "cusps". Places where the probability of finding an electron drops to zero or very near zero. There are nuclear and electron-electron cusps. They can be seen to arise from symmetry properties or directly out of the type of Hamiltonian we use to operate on our Schroedinger equation.

It leads me to think that bond expansion/contraction (spring-like motion) is a variation of conduction-band level oscillations, only with those conduction-band electrons accumulated and concentrated between the atoms

The wavefunction describing the behavior of the electrons, $\Psi$, is separate from the waveunction describing the vibrational motion, $\chi$. There are cases where the vibrational and electronic wavefunctions are coupled [not mathematically separable] but I would not say that the "springlike" motion of the bonds is a result of electronic oscillations directly.

The "spring bond" treatment I introduced to you earlier is only good for predicting the absorption frequencies of the bonds with respect to spectroscopy and such. In reality, the non-electronic degrees of freedom in a molecule are also quantized and are analyzed as wave equations.

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Covalent bonds behave very differently from the conduction band in bulk metals. Electrons in most molecular orbitals cannot communicate. Meaning that an electron in said orbital cannot be conducted through the bond to another orbital. The reason for this is quite mathy, but in quantum chemical treatments we have these things called "cusps". Places where the probability of finding an electron drops to zero or very near zero. There are nuclear and electron-electron cusps.

Generally I had the idea that lower levels of electrons couldn't communicate energy to other levels in the lower levels where emission/absorption is less likely. This seemed a logical step from the fact that metals are better conductors because of the conduction bands being able to absorb/emit lower thresholds of energy quanta. So does "cusp" describe the gaps between orbitals that prevent the electrons from being anywhere except in the specifically allowed orbitals? Is there any reason why these cusps form? Also, does "cusp" describe an actual spatial region where the electrons don't go or is it a description of an abstract curve that represents something indirectly?

The wavefunction describing the behavior of the electrons, $\Psi$, is separate from the waveunction describing the vibrational motion, $\chi$. There are cases where the vibrational and electronic wavefunctions are coupled [not mathematically separable] but I would not say that the "springlike" motion of the bonds is a result of electronic oscillations directly.

I don't know what them being "the result of electronic oscillations directly" would mean? I.e. when the conduction-band electrons oscillate between slightly higher and lower bands, this is not what is going on in the bonds? The conduction-band is a tight concept theoretically because it correlates the quantum-threshholds of electron-level jumping with distance from the nucleus and thus positive charge interaction. It makes some intuitive sense that when an electron is closer to a proton, it would behave more digitally and as it gets farther away, in a more analog way (i.e. with less intense level-jumping). I guess I should just start a new thread on how atomic electrons reconfigure into molecular bonds, because it seems as though their orbital patterns shift in a logical way and that the behavior of the bonds would reflect characteristics of the shifted electron-patterns, but this may be a more complex phenomena than I first thought.

The "spring bond" treatment I introduced to you earlier is only good for predicting the absorption frequencies of the bonds with respect to spectroscopy and such. In reality, the non-electronic degrees of freedom in a molecule are also quantized and are analyzed as wave equations.

What are "non-electronic degrees of freedom?" Do interatomic bonds have quantized energy-levels or are they relatively continuous conductors? Actually, do the conduction-bands of metal generally have spectra as continuous as a black-body, or do they just have spectral lines that are closer together than other levels of electrons? BTW, am I conflating absorption/emission spectra and conductivity in a way that I shouldn't be? Is it correct to think of conduction as occurring in spectral bands the same as emission/absorption?

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What are "non-electronic degrees of freedom?"

vibration, rotation, and translation.

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Someone else posted this (in another thread, I think) but I find it relevant in this thread if anyone is interested:

http://en.wikipedia.org/wiki/Metallic_bond

It supported the directions my thoughts were going in about electron-abundance and electrons behaving like a "sea" of de-localized bonding among the atoms, etc. but now I'm confused about the extent to which there are well-defined bonds between metal atoms and that to which they are "collectively bonded" by free de-localized bonding.

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A bound system means energy is required to free the constituent particles. In this case, break atoms away from a lattice. That's quite different from the electrons moving freely between the atoms — one electron leaves and another generally takes its place and the material remains neutral. That doesn't imply it's easy to break the bond.

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A bound system means energy is required to free the constituent particles. In this case, break atoms away from a lattice. That's quite different from the electrons moving freely between the atoms — one electron leaves and another generally takes its place and the material remains neutral. That doesn't imply it's easy to break the bond.

But what's interesting with regards to metal expanding is that if there are no areas of special concentration between the atoms (i.e. bonds in the sense of plural distinct units), then the vibration among the atoms has to take place through the "collective bonding," which I assume is relatively homogenous throughout the material. I.e. it doesn't sound like there are concentrated bonds between the atoms specifically that vibrate causing the molecules to expand. It sounds more like the lattice bonds all the atoms in the substance together as if the substance were a single large molecule and the 'electron-bath' bonding them behaves like a liquid or gas diffusing energy and by doing so vibrating and expanding.

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